# Generating artificial experimental data to test model fitting software

I wish to test some model fitting software and I would like to generate synthetic datasets for this test. The synthetic data is supposed to originate from a experiment that measures the change in concentration of a substance over time. I can generate error free data for such an experiment using a differential equation model. My question however is what kind of noise should I add so that the data resembles a real experimental dataset? My current two choices are to either add noise from a gaussian or exponential distribution, any preferences? (Eg adding gaussian noise could potentially generate negative concentrations)

My other concern is should the degree of noise be equal for all data points? For example I would imagine there would be more uncertainty in small concentrations that larger ones, simply because it is more difficult to measure small concentrations.

• I'm not sure why Gaussian white noise would necessarily lead to negative values. For example, $\frac{dy}{dt} = \alpha + W_t y$ models a constant rate of growth with noise ($\alpha$ is a positive constant, $W_t$ is white noise). Note that the noise is scaled by the value of $y$, preventing a negative growth rate when $y=0$ and thus preventing negative concentrations. Can you provide more details about your ode? Dec 24, 2013 at 18:39
• Imagine that the true concentration of a substance is 0.1 units. When the concentration is measured some error is introduced so what I actually get is 0.1 +/- error. I could simulate the experiment by drawing a number from a gaussian distribution with mean 0.1 and say an sd of 0.05 and add it to the 0.1 (Assuming the errors are normally distributed). There is however a chance that when I draw the error value and add it to the 0.1 I could end up with a negative concentration. I assume that's how it works. As to the types of ODEs, they are homogeneous and usually nonlinear. Dec 24, 2013 at 18:58